Reverse Euclidean and Gaussian Isoperimetric Inequalities for Parallel Sets With Applications
Reverse Euclidean and Gaussian Isoperimetric Inequalities for Parallel Sets With Applications
The r-parallel set of a set A ⊆ R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> is the set of all points whose distance from A is less than r. In this paper, we show that the surface area of an r-parallel set in R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> with volume at most V is …